A solution of the conjecture about big vertices of minimal-ABC trees

Darko Dimitrov and Zhibin Du

Applied Mathematics and Computation, 2021, vol. 397, issue C

Abstract: The problem of full determination of trees with a minimal value of the ABC index is very hard and famous in mathematical chemistry. A well-known conjecture is that the big vertices (vertices of degree larger than 2, which are not adjacent to a vertex of degree 2) of a tree with a minimal value of the ABC index induce a star graph. Here we give an affirmative answer to this conjecture and thus make a significant step towards the complete characterization of trees with minimal ABC index.

Keywords: Molecular descriptors; Atom-bond connectivity index; Extremal graphs (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:397:y:2021:i:c:s0096300320307712

DOI: 10.1016/j.amc.2020.125818

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